🔢 Part 1: Identifying Prime Numbers

1. Circle all the prime numbers from this list: 7, 9, 11, 15, 17, 21, 23

2. Which of these numbers is NOT prime?

13

19

21

29

3. Explain why 1 is not considered a prime number:

4. Find all prime numbers between 30 and 50:

5. Is 51 a prime number? Show your working and explain your answer:

🧮 Part 2: Prime Factorisation

6. Find the prime factorisation of 60:

7. Express 84 as a product of prime factors:

8. What is the prime factorisation of 100?

2² × 5²

2⁴ × 5²

2² × 5³

2³ × 5²

9. A number has the prime factorisation 2³ × 3² × 5. What is the number?

🔐 Part 3: Real-World Applications

10. Encryption Challenge: A simple encryption code uses two prime numbers, p = 7 and q = 11. Calculate n = p × q, which forms part of the encryption key:

11. Security Puzzle: Explain why large prime numbers are important for internet security and online banking:

12. Critical Thinking: If you were designing a security system and needed to choose between using the number 97 or 99 as part of your code, which would you choose and why?